Modeling cellular systems and aging processes: I. Mathematics of cell system models-a review.

A review of the literature on mathematical models of populations of cellular systems is presented. Continuous, discrete, and stochastic models are presented in a semihistorical manner as a prelude to answering the question of how to model an asynchronously dividing cellular system. This analysis is then broadened, in an attempt to broach the more general question of modeling the distribution of a set or collection of cell properties through an asynchronously dividing cellular system. Such properties might be cell motility, cell cycle length, time to mitosis, or number of epigenetic particles. It is shown that one fruitful approach to this modeling question is a coupled continuous-probabilistic model. The ramifications of this type of formalism are discussed.